In the bowl of a stand mixer fitted with the dough hook attachment, whisk together flours, sugar, yeast, and salt.

Add the warm milk and eggs. With the mixer on low speed, knead until the dough comes together, about 2 minutes. Add butter, a ½-tablespoon at a time, waiting to add the next pieces until the first is fully incorporated. Continue kneading until an elastic and tacky dough forms, about 10 minutes. (Dough will be soft and should feel sticky but not stick to a clean finger when touched. Add a tablespoon or two of additional flour if needed.)

Lightly oil a large bowl, and transfer dough to the oiled bowl. Turn it once to coat the dough in oil and pat it into an even layer. Cover and let it rise in a warm spot until doubled in size, about 45 minutes to 1 hour.

Once the dough has risen, line a baking sheet with parchment paper or a silicone mat.

Lightly flour your surface and turn out the dough. Press it into an even circle, then cut it into 8 pieces (about 100g each).

Using flour as needed, pull the edges of each dough piece into the center and pinch together to create a ball. Turn over and round out with your hands. You don’t need to make the balls very tight, like when shaping dinner rolls. Just get them into a smooth round shape. Place the balls on the baking sheet, spacing them a few inches apart, then flatten them with your palm until they are about 3-inches wide.

Cover with a clean tea towel or plastic wrap, and set aside to rise again until doubled in size, about 30-40 minutes.

Meanwhile, preheat the oven to 400F.

Brush the tops of the risen dough balls lightly with egg wash. Bake for 12 to 15 minutes until tops are golden brown, rotating the pan halfway through baking for more even color. Let the buns cool completely before slicing. Store baked buns in an airtight container for up to 3 days or freeze for up to 3 months.